We propose a novel application of Formal Concept Analysis (FCA) to neural decoding: instead of just trying to figure out which stimulus was presented, we demonstrate how to explore the semantic relationships between the neural representation of large sets of stimuli. FCA provides a way of displaying and interpreting such relationships via concept lattices. We explore the effects of neural code sparsity on the lattice. We then analyze neurophysiological data from high-level visual cortical area STSa, using an exact Bayesian approach to construct the formal context needed by FCA. Prominent features of the resulting concept lattices are discussed, including indications for a product-of-experts code in real neurons.

The peristimulus time historgram (PSTH) and its more continuous cousin, the spike density function (SDF) are staples in the analytic toolkit of neurophysiologists. The former is usually obtained by binning spiketrains, whereas the standard method for the latter is smoothing with a Gaussian kernel. Selection of a bin with or a kernel size is often done in an relatively arbitrary fashion, even though there have been recent attempts to remedy this situation \cite{ShimazakiBinningNIPS2006,ShimazakiBinningNECO2007}. We develop an exact Bayesian, generative model approach to estimating PSHTs and demonstate its superiority to competing methods. Further advantages of our scheme include automatic complexity control and error bars on its predictions.

We present an exact Bayesian treatment of a simple, yet sufficiently general probability distribution model. We consider piecewise-constant distributions P(X) with uniform (second-order) prior over location of discontinuity points and assigned chances. The predictive distribution and the model complexity can be determined completely from the data in a computational time that is linear in the number of degrees of freedom and quadratic in the number of possible values of X. Furthermore, exact values of the expectations of entropies and their variances can be computed with polynomial effort. The expectation of the mutual information becomes thus available, too, and a strict upper bound on its variance. The resulting algorithm is particularly useful in experimental research areas where the number of available samples is severely limited (e.g., neurophysiology). Estimates on a simulated data set provide more accurate results than using a previously proposed method.

The visual system can reliably identify objects even when the retinal image is transformed considerably by commonly occurring changes in the environment. A local learning rule is proposed, which allows a network to learn to generalize across such transformations. During the learning phase, the network is exposed to temporal sequences of patterns undergoing the transformation. An application of the algorithm is presented in which the network learns invariance to shift in retinal position. Such a principle may be involved in the development of the characteristic shift invariance property of complex cells in the primary visual cortex, and also in the development of more complicated invariance properties of neurons in higher visual areas.